1. Field of the Invention
The present invention relates to a profile control method for a sheet-manufacturing process of paper, films, and the like (hereinafter, collectively referred to as sheet) and the system thereof.
Priority is claimed on Japanese Patent Application No. 2006-092756, filed Mar. 30, 2006, the content of which is incorporated herein by reference.
2. Description of the Related Art
In a sheet manufacturing process of paper, films, and the like, to make the quality of sheets in the width direction uniform is the most important factor in characterizing the product quality. For example, T. Sasaki, M. Matsuda, S. Yamamoto, and I. Hashimoto, “Optimizing Control of Basis Weight Profile in Paper Machines based on Virtual Slice-bolt Position,” KAGAKU KOGAKU RONBUNSHU, Vol. 25, No. 6, 1999, pp. 947-954, and Japanese Published Unexamined Patent Application, First Publication No. (JP-A) H2-139488 have disclosed a technology, in which in sheet-making paper by using a paper machine, paper is measured for the basis weight (the weight of paper in grams per square meter: g/m2), while the paper is scanned in the width direction, thereby optimizing the variation (2σ) of deviations with respect to the mean value of basis weight to make the basis weight uniform in the width direction of the paper. Hereinafter, a specific description will be given for the technology.
In this instance, a plurality of basis weight data (t pieces) between one-way scans in the width direction of paper is given as RV(i) (i=1, 2, . . . , t), and a set of data based on deviations between the mean value RVAV of the basis weight data concerned RV(i) and each of the basis weight data RV(i) are called basis weight raw profile. Where the basis weight raw profile is given as R(i), it is expressed as R(i)=RV(i)−RVAV (i=1, 2, . . . , t). Further, of a plurality of actuators (N units), the above basis weight raw profile changes on operation of the kth actuator. In this instance, the number of basis weight data RV(i) corresponding to the center of a change in profile is called a kth actuator position correspondence, which is given as SPT(k). In other words, SPT(k) is an integer value from 1 to t.
Further, virtual actuators (the total number N−1 unit) are defined at an intermediate position of adjacent actuators, and the number of basis weight data RV(i) corresponding to the center of the change in profile due to operation of the virtual actuator is called a virtual actuator position correspondence, which is given as SP(i) (i=1, 2, . . . , 2N−1). In this instance, basis weight raw profiles are averaged with respect to the position of an actually available actuator and that of a virtually defined actuator, thereby defining a virtual actuator corresponding profile P(i) which is expressed by the formula (1) given below.
                                          P            ⁡                          (              i              )                                =                                    1              MPT                        ⁢                                          ∑                                  j                  =                                      -                    h                                                                    +                  h                                            ⁢                                                R                  ⁡                                      (                                                                  SP                        ⁡                                                  (                          i                          )                                                                    +                      j                                        )                                                  ⁢                                                                  ⁢                                  (                                                            i                      =                      1                                        ,                    …                    ⁢                                                                                  ,                                                                  2                        *                        N                                            -                      1                                                        )                                                                    ⁢                                  ⁢                  where          ,                      MPT            =                          a              ⁢                                                          ⁢              first              ⁢                                                          ⁢              odd              ⁢                                                          ⁢              number              ⁢                                                          ⁢              of              ⁢                                                          ⁢              no              ⁢                                                          ⁢              less              ⁢                                                          ⁢              than              ⁢                                                          ⁢                              t                                                      2                    ⁢                    N                                    -                  1                                                                    ⁢                                  ⁢                  h          =                                    MPT              -              1                        2                                              (        1        )            
In the above formula (1), the virtual actuator position correspondence SP(i) is expressed by the following formulae (2) and (3). In other words, an odd-numbered virtual actuator position correspondence is equal to a kth actuator position correspondence, whereas an even-numbered virtual actuator position correspondence is obtained by rounding the mean value of the kth actuator position correspondence of an adjacent actuator to obtain an integer number.SP(2k−1)=SPT(k)   (2)
                              SP          ⁡                      (                          2              ⁢              k                        )                          =                  int          (                                                    SPT                ⁡                                  (                  k                  )                                            +                              SPT                ⁡                                  (                                      k                    +                    1                                    )                                                      2                    )                                    (        3        )                            k=1, . . . , and N (N: the number of actuators)        
As shown in the above formula (1), the virtual actuator corresponding profile P(i) is a profile consisting of points which is two times the total number of actuators (N) minus 1 (i.e., N×2−1), which is obtained by averaging basis weight raw profiles with respect to the position of an actually available actuator and that of a virtually defined actuator. Each of the actuators is controlled, with the objective of optimizing mountain/valley portions of the above-described virtual actuator corresponding profile P(i), that is, variation (2σ) of deviations with respect to mean values, thereby making it possible to make the basis weight uniform in the width direction of paper.
In this instance, the manipulated value of each of the actuators is given as X(j) (j=1, 2, . . . , N). In general, where each of the actuators arranged in the width direction is operated, a profile is changed not only at a position corresponding to the thus operated actuator but also in the vicinity thereof. This phenomenon is called a width-direction process interference. Where a variation of an ith virtual actuator corresponding profile P(i) with respect to the above-described manipulated value X(j) is given as W(i,j) and a matrix expressing the width-direction process interference (process interference matrix) is defined as W={W(i,j)}, a matrix P of the virtual actuator corresponding profile is expressed by the formula (4) shown below.P=X·tW+P0 (tW is a transposed matrix of W)   (4)where,
P=(P(1),P(2), . . . , P(2·N−1)): Virtual actuator corresponding profile
P0=(P0(1), P0(2), . . . , P0(2·N−1)): Initial value of the virtual actuator corresponding profile
X=(X(1),X(2), . . . ,X(N)): Manipulated value
  W  =            [                                                                  W                ⁡                                  (                                      1                    ,                    1                                    )                                            ⁢                                                          ⁢                              W                ⁡                                  (                                      1                    ,                    2                                    )                                            ⁢                                                          ⁢              …              ⁢                                                          ⁢                              W                ⁡                                  (                                      1                    ,                    N                                    )                                                                                                        W              ⁡                              (                                  2                  ,                  1                                )                                                                                                        W                ⁡                                  (                                                                                    2                        ·                        N                                            -                      1                                        ,                    1                                    )                                            ⁢                                                          ⁢              …              ⁢                                                          ⁢                              W                ⁡                                  (                                                                                    2                        ·                        N                                            -                      1                                        ,                    N                                    )                                                                        ]        ⁢          :      Process interference matrix
Further, the virtual actuator corresponding profile P(i) expresses at all times a deviation with respect to a mean value. Thus, assuming that the mean value of the virtual actuator corresponding profile P(i) is zero, an evaluation function E(X) indicating a variation of the deviation with respect to the above mean value is expressed by the formula (5) given below. Further, a gradient ∇E(X) of the evaluation function E(X) is expressed by the formula (6) given below.
                                                                        E                ⁡                                  (                  X                  )                                            =                                                ∑                                      i                    =                    1                                                                              2                      ·                      N                                        -                    1                                                  ⁢                                                      P                    ⁡                                          (                      i                      )                                                        2                                                                                                        =                              P                ·                                                                           t                                    ⁢                  P                                                                                                        =                                                (                                                                                    X                        t                                            ⁢                      W                                        +                                          P                      0                                                        )                                ·                                                                           t                                    ⁢                                      (                                                                                            X                          t                                                ⁢                        W                                            +                                              P                        0                                                              )                                                                                                                          =                                                                    X                    t                                    ⁢                                      W                    ·                                          W                      t                                                        ⁢                  X                                +                                                      P                    0                                    ⁢                                      W                    t                                    ⁢                  X                                +                                                      X                    t                                    ⁢                                      W                    t                                    ⁢                                      P                    0                                                  +                                                      P                    0                                    ⁢                                      P                    0                                                                                    t                                                                                                          (        5        )            Assuming
            ∇              E        ⁡                  (          X          )                      =          (                                    ∂                          E              ⁡                              (                X                )                                                          ∂                          X              ⁡                              (                1                )                                                    ,                              ∂                          E              ⁡                              (                X                )                                                          ∂                          X              ⁡                              (                2                )                                                    ,        …        ⁢                                  ,                              ∂                          E              ⁡                              (                X                )                                                          ∂                          X              ⁡                              (                N                )                                                        )        ,The following is obtained.
                                                                        ∇                                  E                  ⁡                                      (                    X                    )                                                              =                                                2                  ⁢                                      X                    t                                    ⁢                                      W                    ·                    W                                                  +                                  2                  ⁢                                      P                    0                                    ⁢                  W                                                                                                        =                                                2                  ⁢                                                            (                                              P                        -                                                  P                          0                                                                    )                                        ·                    W                                                  +                                  2                  ⁢                                      P                    0                                    ⁢                  W                                                                                                        =                              2                ⁢                                  P                  ·                  W                                                                                        (        6        )            
In this instance, the changed manipulated value ΔX for making the evaluation function E(X) small most rapidly (in other words, minimizing the variation of deviations in the virtual actuator corresponding profile) is expressed based on the steepest descent method by using a sufficiently small positive value E to give the formula (7), which is also expressed in a scalar form as the formula (8) shown below.
                              Δ          ⁢                                          ⁢          X                =                                            -                              ɛ                2                                      ·                          ∇                              E                ⁡                                  (                  X                  )                                                              =                                    -              ɛ                        ·            P            ·            W                                              (        7        )                                          Δ          ⁢                                          ⁢                      X            ⁡                          (              j              )                                      =                              -            ɛ                    ·                                    ∑                              l                =                1                                                              2                  ·                  N                                -                1                                      ⁢                                                            P                  ⁡                                      (                    i                    )                                                  ·                                  W                  ⁡                                      (                                          i                      ,                      j                                        )                                                              ⁢                                                          ⁢                              (                                                      j                    =                    1                                    ,                  …                  ⁢                                                                          ,                  N                                )                                                                        (        8        )            
In other words, based on a plurality of basis weight data between one-way scans, a virtual actuator corresponding profile P(i) is calculated from the above formula (1), and the changed manipulated value ΔX of each actuator is also calculated from the above formula (8), thereby the changed manipulated value ΔX is used to control each of the actuators. It is, therefore, possible to make the basis weight uniform in the width direction of paper. Further, the technology disclosed in Sasaki et al. and JP-A 02-139488 is applicable as a profile control not only to paper but also to other sheets such as films in the manufacturing process.
Further, Japanese Published Unexamined Patent Application, First Publication No. (JP-A) 2005-186377 has disclosed a film-thickness control method for providing a preferable film winding shape by uniformizing local projections made on a thickness profile in the width direction of film in manufacturing processes. According to this film-thickness control method, first, a film pushed out from a slit-shaped film discharge port mounted on a T die is measured for thickness, while the film is scanned in the width direction, thereby obtaining a thickness profile indicating the variation of deviations with respect to the mean value of the thickness. Then, a first correction control value is determined so that the variation of the thickness profile will fall within a permissible range of use, and a second correction control value is determined so that projections of the thickness profile will fall within the permissible range of use. On the basis of the first correction control value and the second correction control value, the clearance of the film discharge port on the T die is controlled. More specifically, a plurality of adjusting bolts having the same function as the actuator in the above-described paper machine are arranged along a lip portion of the film discharge port. Each of the adjusting bolts is controlled for a vertical movement based on the first correction control value and the second correction control value, by which load applied to the lip portion is adjusted to control the clearance of the film discharge port and uniformize the film thickness.
Incidentally, according to the technology disclosed in the above Sasaki et al. and JP-A 02-139488, it is possible to uniformize a profile for the width direction of sheets by defining a virtual actuator corresponding profile P(i) and controlling each actuator with the objective of optimizing the variation (2σ) mainly based on the mean value of the profile concerned. However, the following problems exist regarding the quality of an entire roll finally wound up.
In processes of manufacturing a plastic film, in particular, a greater importance is placed on a preferable film winding shape after being wound up to a roll, rather than on the variation of thickness profiles in the width direction of the film. For example, where there are at all times projections greater than those in the vicinity at the same place of a thickness profile, the projections come to the surface as lumps on winding up the film to the roll, thus resulting in the deteriorated quality of the film winding shape in the roll. According to the technology disclosed in Sasaki et al. and JP-A 02-139488, there are some cases where the above-described projections which are greater than those in the vicinity may remain on the film.
On the other hand, according to the technology disclosed in JP-A 2005-186377, after a first correction control value is determined, a thickness profile variation is estimated by referring to a model, and a second correction control value is also determined for making the projections uniform in height. This method requires a greater calculation amount to result in an increased processing load on a calculating unit, which is problematic.
Further, where there is an unexpectedly great difference between the thickness profile variation calculated by referring to the model and an actual thickness profile variation due to disturbance, another problem is posed that a sufficient control performance is not maintained.